Densities and Viscosities for the Ternary Mixtures of exo

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Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Densities and Viscosities for the Ternary Mixtures of exo-Tetrahydrodicyclopentadiene (1) + Isopropylcyclohexane (2) + Methyl Laurate (3) and Corresponding Binaries Wenqi Zhao,† Yitong Dai,† Haiyun Sun,‡ Yongsheng Guo,*,† and Wenjun Fang† †

Department of Chemistry, Zhejiang University, Hangzhou 310058, China Beijing Key Laboratory of Research and Application for Aerospace Green Propellants, Beijing Institute of Aerospace Testing Technology, Beijing 100000, China

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‡

S Supporting Information *

ABSTRACT: Biofuel mixed with fossil jet fuels has a lot of potential in applications of jet fuel extenders. To understand the fundamental properties of this typical mixture, measurements on densities and viscosities for the ternary model system of exo-tetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2) + methyl laurate (3) and three corresponding binary mixtures have been implemented over the entire composition range at eleven different temperatures from 293.15 to 343.15 K. The excess molar volumes (VEm) and viscosity deviations (Δη) of binary mixtures were calculated and correlated by the Redlich−Kister equation, while the corresponding data of ternary mixtures were fitted to Nagata−Tamura, Cibulka, Singh, and Redlich−Kister equations. Furthermore, the variations of VEm and Δη were represented and discussed based on molecular interactions and structural effects in detail.

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INTRODUCTION During the development process of aviation industry, the economic and environmental problems caused by excessive fuel consumption have posed a threat all over the world. A strategy that has come into increasing focus recently is to exploit different sustainable energy sources to replace conventional petroleum fuels.1,2 Among these alternative fuel sources, biofuels are considered as the strongest contender because of their significant reduction in greenhouse gas emission and production cost.3−5 Biodiesel, a mixture of long-chain methyl or ethyl monoesters, is obtained by transesterification of various biomass with small-molecule alcohols such as methanol or ethanol. As a typical category of biofuels, it can act as a renewable energy source and also as an oxygenated additive to significantly improve the combustion performance.6,7 Virtually, biodiesel mixed with fossil jet fuel shows a lot of potential in applications of jet fuel extenders. Dagaut and GaiL8 studied the oxidation behavior of Jet A-1 and biokerosene (rapeseed oil methyl ester/Jet A-1 mixture) and found that there was no major modification of product distribution. Dunn9 observed that JP-8/JP-8+100 blended with winterized methyl soyate yielded substantial cloud point reduction which resulted in allowable increasing of aircraft flight height. Korres et al.10 showed that a certain amount of biodiesel mixed in JP-5 could improve significant properties for diesel engines such as the particulate matter emissions. Normally, the knowledge of the fundamentally thermophysical properties is of great significance before putting blended © XXXX American Chemical Society

fuel into service, owing to the close connection between physical properties and engineering performance.11−13 Density is a vital index which is directly related to the volumetric energy of fuel. It is also crucial for the injection unit which should convey the amount of fuel precisely adjusted to provide proper combustion.14 Viscosity is another important parameter associated with practical unit operations.15,16 Fuel with high viscosity will have a negative impact on the transportation, spray, and atomization process. Conversely, fuel with low viscosity may affect the lubrication of moving parts and lead to leakage or excessive wear. Despite the fact that the thermophysical properties of biodiesel have been reported,17−19 the literature about corresponding properties of mixing systems between biodiesel and conventional jet fuels is extremely scarce. Considering this, the standard missile fuel JP-10 (exotetrahydrodicyclopentadiene) used by U. S. Navy and Air Force, isopropylcyclohexane (predominant component in jet fuels20) and methyl laurate (predominant component in coconut biodiesel21), as the model fuel, in the present work, were mixed over the entire composition range. Densities and viscosities of the ternary mixtures and corresponding binary mixtures were measured at temperatures T = (293.15−343.15) K and atmospheric pressure p = 0.1 MPa. Meanwhile, the excess molar volumes (VEm) and the viscosity deviations (Δη) were Received: May 4, 2019 Accepted: August 5, 2019

A

DOI: 10.1021/acs.jced.9b00397 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

method. It can be calculated according to eq 1. The accuracy of efflux time of the metal ball is within 0.001 s, and the relative uncertainty of viscosity23 in this work is estimated to be 0.01.

calculated and analyzed in detail, which was expected to provide some basic information of biodiesel in applications of jet fuel extenders.

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η = k(ρball − ρ)t

EXPERIMENTAL SECTION Materials. Three chemicals (exo-tetrahydrodicyclopentadiene, isopropylcyclohexane, and methyl laurate) were used for preparing and mixture samples in this work. The molecular structure and detailed specifications of each chemical are presented in Figure 1 and Table 1. All the chemicals were

(1)

where η is the dynamic viscosity of the sample. k represents the constant of the viscometer. ρball and ρ are the densities of the metal ball and the sample, respectively. t denotes the average ball falling time of the sample.

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RESULTS AND DISCUSSION The values of densities and viscosities of three pure components at different experimental temperatures (T = 293.15− 343.15 K) are listed in the Table 2, as well as the corresponding literature data. The absolute average relative deviations (% AARD) calculated according to eq 2 indicate good agreement between our work and other reported works. P −P i 100 yz zz∑ lit % AARD = jjj Plit k n { i=1 n

(2)

In this equation, Plit means the literature data of density or viscosity, while P means the experimental data of density or viscosity in this work. Volumetric and Viscometric Properties of the Binary Mixtures. The experimental densities and viscosities of three binary mixtures, exo-tetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2), exo-tetrahydrodicyclopentadiene (1) + methyl laurate (2), and isopropylcyclohexane (1) + methyl laurate (2), over the entire composition range at different temperatures (T = 293.15−343.15 K), are listed in Tables 3 and 4, respectively. It can be easily found that both densities and viscosities of all mixture samples decrease with the increase of testing temperature. Furthermore, the excess molar volumes (VEm) and viscosity deviations (Δη) of corresponding mixture samples are calculated using the eqs 3 and 4 and shown in Tables S1 and S2, respectively. ÅÄÅ ÑÉ n ÅÅij 1 yz ij 1 yzÑÑÑ E j z Å j z Vm = ∑ xiMiÅÅÅjj zz − jjj zzzÑÑÑÑ ÅÅk ρ { k ρi {ÑÑ (3) i=1 ÅÇ ÑÖ

Figure 1. Molecular structure of (a) exo-tetrahydrodicyclopentadiene, (b) isopropylcyclohexane, and (c) methyl laurate.

obtained through commercial means. The purities of them were checked by Agilent 7890A/5975C gas chromatography− mass spectrometry (GC−MS), and the comparison of experimental densities and viscosities of three chemicals with the literature data was shown in Table 2. The results confirmed the availability of all compounds, and no further purification was employed in this study. The mixture samples were freshly prepared just before determined. Methods. All mixture samples were prepared by the weighting method using a Mettler Toledo AL204 analytical balance. The stated precision of analytical balance is 0.0001 g, and the combined standard uncertainty of mole fraction (x) is calculated to be within 0.0001. Densities and viscosities of samples were measured at eleven different temperatures (T) ranging from 293.15 to 343.15 K and atmospheric pressure (p = 0.1 MPa) in this work. The temperature is balanced by an automatic temperature control unit of densimeter and viscometer with an uncertainty of 0.01 K. The atmospheric pressure is monitored by a Fortin barometer indicating a fluctuation within 0.5 kPa. The densities (ρ) of all samples were determined using a DMA 5000 M densimeter (Anton Paar, Austria). The measurement process was carried out following the self-test and calibration procedure using dry air and ultrapure water. Considering the measurement uncertainty (±0.00005 g·cm−3) and sample purity, the relative uncertainty of experimental densities22 is 0.0003. The viscosities (η) of all samples were obtained using an AMVn viscometer (Anton Paar, Austria) by the falling ball

n

Δη = η −

∑ xiηi

(4)

i=1

In the above equations, n denotes the number of components in mixture samples; xi and Mi denote the mole fraction and molar mass of component i, respectively; ρi and ηi denote the density and viscosity of component i, respectively; ρ and η denote the density and viscosity of mixture sample, respectively. The excess molar volumes and viscosity deviations of the three binary mixtures (i + j) are fitted as a function of the composition by a Redlich−Kister type equation

Table 1. Specification of Chemicals in This Work compound exo-tetrahydrodicyclopentadiene isopropylcyclohexane methyl laurate

source a

Yangli b TCI c Aladdin

CAS number

provided mass fraction purity

measured mass fraction purity

analysis method

2825-82-3 696-29-7 111-82-0

≥0.98 ≥0.99 0.99

0.985 0.998 0.998

GC−MS GC−MS GC−MS

a

Yangli is the abbreviation of Hangzhou Yangli Petrochemical Company. bTCI is the abbreviation of Tokyo Chemical Industry. cAladdin is the abbreviation of Aladdin Industrial corporation. B



Article

Table 2. Comparison between Measured and Literature Data of Densities ρ and Viscosities η for the Pure Components at Corresponding Temperatures and Pressure p = 0.1 MPaa property ρ/g·cm−3

η/mPa·s

ρ/g·cm−3

T/K

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exo-Tetrahydrodicyclopentadiene 293.15 0.93585 0.935758b, 0.93574c, 0.93572d, 0.9357e 298.15 0.93195 0.931867b, 0.93186c, 0.93184d, 0.9318e 303.15 0.92806 0.927961b, 0.92795c, 0.92794d, 0.9280e 308.15 0.92417 0.924049b, 0.92402d, 0.9241e 313.15 0.92026 0.92013b, 0.92013c, 0.92011d, 0.9202e 318.15 0.91633 0.91618d, 0.9163e 323.15 0.91240 0.91214c, 0.9125e 328.15 0.90846 0.9086e 333.15 0.90452 0.90425c, 0.9046e 338.15 0.90056 0.9006e 343.15 0.89661 0.89632c, 0.8967e 293.15 2.994 2.992d, 3.0582e, 2.974f 298.15 2.712 2.710d, 2.7673e, 2.694f 303.15 2.470 2.467d, 2.5153e, 2.454f 308.15 2.259 2.255d, 2.2957e, 2.243f 313.15 2.073 2.069d, 2.1034e, 2.059f 318.15 1.909 1.907d, 1.9343e 323.15 1.764 1.762c, 1.7848e 328.15 1.635 1.6515e 333.15 1.519 1.514c, 1.5321e 338.15 1.416 1.4252e 343.15 1.322 1.318c, 1.3284e Isopropylcyclohexane 293.15 0.80211 0.80214g, 0.80221h 298.15 0.79822 0.79824g, 0.79833h 303.15 0.79432 0.79434g, 0.79444h 308.15 0.79041 0.79043g 313.15 0.78650 0.78651g 318.15 0.78257 0.78259g 323.15 0.77864 0.77866g 328.15 0.77469 0.77472g 333.15 0.77073 0.77077g

AARD/%

property

0.013 0.012

η/mPa·s

0.010 0.012 0.013 0.010 0.020 0.015 0.019 0.004 0.021 0.944 0.913 0.859 0.824 0.767 0.706 0.639 1.025 0.593 0.671 0.393

ρ/g·cm−3

η/mPa·s

0.008 0.008 0.008 0.002 0.002 0.002 0.003 0.004 0.005

T/K 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

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Isopropylcyclohexane 0.76676 0.76681g 0.76278 0.76284g 1.098 1.093g, 1.097i 1.020 1.016g 0.950 0.947g 0.889 0.886g 0.833 0.831g, 0.824i 0.783 0.782g 0.738 0.738g 0.697 0.698g 0.660 0.661g 0.626 0.628g 0.596 0.598g Methyl Laurate 0.86922 0.86916j, 0.8693k 0.86530 0.86523j 0.86137 0.86130j, 0.8614k 0.85744 0.85737j 0.85351 0.85344j, 0.8535k 0.84958 0.84951j 0.84565 0.84557j, 0.8458k 0.84172 0.84163j 0.83778 0.83769j, 0.8376k 0.83384 0.83374j 0.82990 0.82979j 3.120 3.110j, 3.1519l 2.778 2.786j, 2.7895l 2.491 2.497j, 2.4907l 2.250 2.254j, 2.2437l 2.044 2.048j, 2.0346l 1.866 1.865j, 1.8624l 1.712 1.698j, 1.7023l 1.577 1.562j, 1.5640l 1.458 1.442j, 1.4438l 1.353 1.340j, 1.3380l 1.260 1.247j, 1.2455l

AARD/% 0.007 0.008 0.281 0.372 0.357 0.295 0.632 0.117 0.001 0.120 0.083 0.249 0.381 0.008 0.008 0.006 0.008 0.005 0.008 0.014 0.010 0.016 0.012 0.013 0.667 0.367 0.126 0.229 0.329 0.134 0.701 0.887 1.054 1.053 1.095

a e

Standard uncertainties u are u(p) = 0.50 kPa, u(T) = 0.01 K, ur(ρ) = 0.0003, ur(η) = 0.01. bReference 31. cReference 32. dReference 33. Reference 34. fReference 35. gReference 20. hReference 36. iReference 37. jReference 21. kReference 38. lReference 39.

Table 3. Measured Densities (ρ) at Different Mole Fractions (x1) for the Binary Mixtures of exo-Tetrahydrodicyclopentadiene (1) + Isopropylcyclohexane (2); exo-Tetrahydrodicyclopentadiene (1) + Methyl Laurate (2); and Isopropylcyclohexane (1) + Methyl Laurate (2) at Temperatures T = (293.15−343.15) K and Pressure p = 0.1 MPaa ρ/g·cm−3 x1

293.15 K

298.15 K

0.0000 0.1002 0.1999 0.3001 0.4000 0.5000 0.5999 0.7001 0.8003 0.8999 1.0000

0.80211 0.81495 0.82783 0.84092 0.85410 0.86742 0.88087 0.89445 0.90822 0.92193 0.93585

0.79822 0.81106 0.82393 0.83701 0.85019 0.86350 0.87695 0.89054 0.90431 0.91804 0.93195

0.0000 0.1012

0.86922 0.87298

0.86530 0.86906

303.15 K

308.15 K

313.15 K

318.15 K

323.15 K

328.15 K

exo-Tetrahydrodicyclopentadiene (1) + Isopropylcyclohexane (2) 0.79432 0.79041 0.78650 0.78257 0.77864 0.77469 0.80715 0.80323 0.79931 0.79538 0.79144 0.78749 0.82002 0.81610 0.81217 0.80823 0.80429 0.80033 0.83309 0.82918 0.82524 0.82130 0.81735 0.81339 0.84627 0.84235 0.83842 0.83447 0.83052 0.82656 0.85959 0.85567 0.85174 0.84779 0.84384 0.83988 0.87303 0.86911 0.86517 0.86123 0.85728 0.85332 0.88663 0.88271 0.87878 0.87484 0.87089 0.86693 0.90041 0.89650 0.89257 0.88863 0.88468 0.88073 0.91414 0.91024 0.90631 0.90238 0.89844 0.89450 0.92806 0.92417 0.92026 0.91633 0.91240 0.90846 exo-Tetrahydrodicyclopentadiene (1) + Methyl Laurate (2) 0.86137 0.85744 0.85351 0.84958 0.84565 0.84172 0.86513 0.86120 0.85727 0.85334 0.84941 0.84548 C

333.15 K

338.15 K

343.15 K

0.77073 0.78353 0.79637 0.80942 0.82259 0.83591 0.84935 0.86297 0.87677 0.89054 0.90452

0.76676 0.77955 0.79239 0.80545 0.81861 0.83193 0.84537 0.85899 0.87280 0.88658 0.90056

0.76278 0.77557 0.78840 0.80145 0.81462 0.82794 0.84139 0.85501 0.86882 0.88261 0.89661

0.83778 0.84152

0.83384 0.83761

0.82990 0.83367



Article

Table 3. continued ρ/g·cm−3 x1

293.15 K

298.15 K

303.15 K

0.2004 0.3001 0.4004 0.5021 0.6003 0.7003 0.8001 0.8991 1.0000

0.87703 0.88155 0.88665 0.89247 0.89883 0.90619 0.91462 0.92433 0.93585

0.87311 0.87764 0.88273 0.88855 0.89491 0.90227 0.91070 0.92041 0.93195

0.86919 0.87372 0.87882 0.88464 0.89099 0.89835 0.90678 0.91649 0.92806

0.0000 0.1008 0.2004 0.3006 0.4002 0.5004 0.6003 0.7001 0.8000 0.9001 1.0000

0.86922 0.86442 0.85935 0.85391 0.84811 0.84182 0.83505 0.82773 0.81983 0.81128 0.80211

0.86530 0.86050 0.85545 0.85002 0.84423 0.83795 0.83118 0.82386 0.81596 0.80740 0.798224

0.86137 0.85659 0.85155 0.84613 0.84033 0.83406 0.82730 0.81998 0.81208 0.80352 0.794323

308.15 K

313.15 K

318.15 K

323.15 K

328.15 K

exo-Tetrahydrodicyclopentadiene (1) + Methyl Laurate (2) 0.86527 0.86134 0.85741 0.85348 0.84954 0.86980 0.86587 0.86195 0.85802 0.85409 0.87490 0.87097 0.86705 0.86312 0.85918 0.88072 0.87679 0.87286 0.86893 0.86499 0.88707 0.88314 0.87921 0.87527 0.87133 0.89442 0.89049 0.88656 0.88262 0.87867 0.90285 0.89892 0.89499 0.89105 0.88710 0.91257 0.90864 0.90470 0.90076 0.89682 0.92417 0.92026 0.91633 0.91240 0.90846 Isopropylcyclohexane (1) + Methyl Laurate (2) 0.85744 0.85351 0.84958 0.84565 0.84172 0.85267 0.84876 0.84484 0.84091 0.83699 0.84764 0.84373 0.83982 0.83590 0.83198 0.84223 0.83833 0.83442 0.83051 0.82659 0.83644 0.83254 0.82863 0.82472 0.82081 0.83017 0.82628 0.82238 0.81848 0.81456 0.82341 0.81952 0.81562 0.81172 0.80780 0.81609 0.81220 0.80830 0.80439 0.80048 0.80819 0.80429 0.80039 0.79647 0.79255 0.79962 0.79572 0.79181 0.78789 0.78395 0.790414 0.786498 0.782571 0.778635 0.774689

333.15 K

338.15 K

343.15 K

0.84561 0.85015 0.85524 0.86105 0.86738 0.87472 0.88315 0.89287 0.90452

0.84166 0.84621 0.85130 0.85710 0.86343 0.87077 0.87919 0.88891 0.90056

0.83772 0.84226 0.84735 0.85315 0.85948 0.86681 0.87523 0.88494 0.89661

0.83778 0.83306 0.82806 0.82267 0.81689 0.81064 0.80388 0.79655 0.78862 0.78001 0.770731

0.83384 0.82913 0.82413 0.81874 0.81296 0.80671 0.79995 0.79262 0.78468 0.77606 0.76676

0.82990 0.82519 0.82019 0.81481 0.80903 0.80278 0.79601 0.78867 0.78073 0.77209 0.762777

a

Standard uncertainties u are u(p) = 0.50 kPa, u(T) = 0.01 K, uc(x) = 0.0001, ur(ρ) = 0.0003.

Table 4. Measured Viscosities (η) at Different Mole Fractions (x1) for the Binary Mixtures of exo-Tetrahydrodicyclopentadiene (1) + Isopropylcyclohexane (2); exo-Tetrahydrodicyclopentadiene (1) + Methyl Laurate (2); and Isopropylcyclohexane (1) + Methyl Laurate (2) at Temperatures T = (293.15−343.15) K and Pressure p = 0.1 MPaa η/mPa·s x1

293.15 K

298.15 K

0.0000 0.1002 0.1999 0.3001 0.4000 0.5000 0.5999 0.7001 0.8003 0.8999 1.0000

1.098 1.194 1.305 1.431 1.578 1.741 1.938 2.165 2.421 2.706 2.994

1.020 1.106 1.206 1.320 1.451 1.597 1.775 1.976 2.205 2.456 2.712

0.0000 0.1012 0.2004 0.3001 0.4004 0.5021 0.6003 0.7003 0.8001 0.8991 1.0000

3.120 3.062 3.012 2.973 2.927 2.896 2.874 2.864 2.877 2.909 2.994

2.778 2.730 2.690 2.659 2.625 2.599 2.585 2.580 2.595 2.628 2.712

0.0000 0.1008 0.2004 0.3006 0.4002 0.5004

3.120 2.862 2.608 2.365 2.139 1.930

2.778 2.558 2.342 2.133 1.937 1.756

303.15 K

308.15 K

313.15 K

318.15 K

323.15 K

328.15 K

exo-Tetrahydrodicyclopentadiene (1) + Isopropylcyclohexane (2) 0.950 0.889 0.833 0.783 0.738 0.697 1.029 0.960 0.898 0.842 0.793 0.748 1.119 1.042 0.973 0.911 0.855 0.805 1.222 1.135 1.058 0.989 0.927 0.872 1.340 1.242 1.156 1.078 1.009 0.946 1.471 1.361 1.265 1.178 1.100 1.029 1.631 1.506 1.397 1.298 1.210 1.131 1.812 1.670 1.543 1.431 1.331 1.242 2.016 1.853 1.709 1.581 1.467 1.367 2.241 2.055 1.891 1.746 1.616 1.503 2.470 2.259 2.073 1.909 1.764 1.635 exo-Tetrahydrodicyclopentadiene (1) + Methyl Laurate (2) 2.491 2.250 2.044 1.866 1.712 1.577 2.454 2.218 2.018 1.844 1.693 1.561 2.419 2.191 1.994 1.824 1.676 1.546 2.397 2.173 1.980 1.813 1.668 1.539 2.369 2.152 1.963 1.799 1.656 1.531 2.349 2.134 1.951 1.789 1.647 1.523 2.339 2.129 1.946 1.787 1.647 1.524 2.338 2.130 1.949 1.791 1.652 1.530 2.356 2.149 1.969 1.811 1.672 1.548 2.388 2.183 2.001 1.841 1.702 1.577 2.470 2.259 2.073 1.909 1.764 1.635 Isopropylcyclohexane (1) + Methyl Laurate (2) 2.491 2.250 2.044 1.866 1.712 1.577 2.303 2.088 1.904 1.743 1.602 1.479 2.117 1.926 1.759 1.616 1.490 1.379 1.936 1.768 1.621 1.493 1.380 1.281 1.765 1.617 1.488 1.375 1.274 1.185 1.606 1.476 1.363 1.262 1.174 1.094 D

333.15 K

338.15 K

343.15 K

0.660 0.708 0.760 0.821 0.889 0.966 1.060 1.161 1.275 1.402 1.519

0.626 0.670 0.719 0.775 0.838 0.909 0.995 1.088 1.193 1.309 1.416

0.596 0.636 0.681 0.733 0.791 0.856 0.936 1.022 1.119 1.225 1.322

1.458 1.444 1.432 1.427 1.419 1.412 1.414 1.420 1.438 1.466 1.519

1.353 1.341 1.330 1.326 1.319 1.314 1.317 1.323 1.340 1.367 1.416

1.260 1.249 1.239 1.236 1.231 1.226 1.229 1.235 1.252 1.276 1.322

1.458 1.371 1.281 1.193 1.106 1.024

1.353 1.276 1.193 1.113 1.035 0.960

1.260 1.189 1.115 1.042 0.971 0.902



Article

Table 4. continued η/mPa·s x1 0.6003 0.7001 0.8000 0.9001 1.0000

293.15 K 1.728 1.546 1.378 1.229 1.098

298.15 K 1.579 1.419 1.271 1.137 1.020

303.15 K 1.450 1.308 1.176 1.056 0.950

308.15 K

313.15 K

318.15 K

323.15 K

Isopropylcyclohexane (1) + Methyl Laurate (2) 1.338 1.239 1.152 1.074 1.211 1.126 1.050 0.981 1.093 1.018 0.952 0.893 0.984 0.920 0.863 0.812 0.889 0.833 0.783 0.738

328.15 K

333.15 K

338.15 K

343.15 K

1.004 0.920 0.840 0.765 0.697

0.941 0.865 0.791 0.723 0.660

0.885 0.815 0.747 0.685 0.626

0.833 0.769 0.707 0.650 0.596

a

Standard uncertainties u are u(p) = 0.50 kPa, u(T) = 0.01 K, uc(x) = 0.0001, ur(η) = 0.01.

Figure 2. Excess molar volumes, VEm, as a function of mole fraction of component 1 for the binary systems of (a) exo-tetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2); (b) exo-tetrahydrodicyclopentadiene (1) + methyl laurate (2); and (c) isopropylcyclohexane (1) + methyl laurate (2) at 0.1 MPa and eleven different temperatures: ■, 293.15 K; ●, 298.15 K; ▲, 303.15 K; ▼, 308.15 K; ⧫, 313.15 K; ◀, 318.15 K; ▶, 323.15 K; ⬢, 328.15 K; ★, 333.15 K; ◑, 338.15 K; ◮, 343.15 K;, the Redlich−Kister correlations.

ÄÅ É ÅÅ ∑ (Y − Y )2 ÑÑÑ1/2 cal Å ÑÑ σ = ÅÅÅ ÑÑ ÅÅÅ ÑÑÑ n − k Ç Ö

n

Yij = xixj∑ Ai (xi − xj)i i=0

(5)

where Yij stands for the excess molar volume or viscosity deviation of the binary mixture; xi and xj stand for the mole fraction of component i and j of the binary mixture; Ai stands for the polynomial coefficient obtained by the leastsquares correlation and F-test; n stands for the number of polynomial coefficients, which is based on the standard deviations (σ) calculated by eq 6. The results of these coefficients as well as standard deviations are listed in Table S5 in detail.

(6)

In the above equation, n and k are the number of experimental data points and fitted polynomial coefficient, respectively. Visually, the changes of excess molar volumes depending on the mole fraction (xi) for the three binary mixtures, at eleven different temperatures, are shown in Figure 2. It can be observed that the excess molar volumes for the binary mixture of exo-tetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2) are all negative over the entire composition range, and E



Article

Figure 3. Viscosity deviations, Δη, as a function of component 1 for the binary systems of (a) exo-tetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2); (b) exo-tetrahydrodicyclopentadiene (1) + methyl laurate (2); and (c) isopropylcyclohexane (1) + methyl laurate (2) at 0.1 MPa and eleven different temperatures: ■, 293.15 K; ●, 298.15 K; ▲, 303.15 K; ▼, 308.15 K; ⧫, 313.15 K; ◀, 318.15 K; ▶, 323.15 K; ⬢, 328.15 K; ★, 333.15 K; ◑, 338.15 K; ◮, 343.15 K;, the Redlich−Kister correlations.

containing strong polar groups of CO and C−O. Among the molecules, there exists strong dipole−dipole electrostatic attraction generally called orientation force. While nonpolar molecules, such as exo-tetrahydrodicyclopentadiene and isopropylcyclohexane, make contact with methyl laurate, the electrostatic attraction will weaken, and the distance between two polar molecules becomes larger.27,28 This phenomenon indicates that the VEm of binary mixtures containing methyl laurate are positive values. Interestingly, the VEm values of the binary mixture exo-tetrahydrodicyclopentadiene (1) + methyl laurate (2) are slightly larger than those of the mixture isopropylcyclohexane (1) + methyl laurate (2), which might be on account of the effect of dispersion force. With increasing molecular mass, dispersion force can be stronger and give more positive values of VEm. The viscosity deviations depended on the mole fraction (xi) for the three binary mixtures, at eleven different temperatures, are illustrated in Figure 3. It can be found that the Δη of binary mixtures including methyl laurate are negative over the entire composition range, and the maximum absolute values of Δη will be reached at about the mole fraction of x1 = 0.6 and 0.5, respectively. The negative Δη is presented owing to the breaking of dipole−dipole interactions during the mixing process.

the minimum value of this mixture appear at about the mole fraction of x1 = 0.5. On the contrary, the other binary mixtures exhibit positive VEm values at all measured temperatures and composition range, while the maximum values are both near x1 = 0.6. Generally, the variation of VEm is mainly influenced by chemical interaction force, intermolecular force, and molecular structure according to accepted theories.24−26 For the binary mixtures studied in this work, there are no specific chemical bond between different components. As a consequence, the results of VEm can be ascribed to the effect of intermolecular force and molecular structure. More specifically, exo-tetrahydrodicyclopentadiene is a three-ring cyclic alkane, while isopropylcyclohexane has only one single ring with a side chain. When the two kinds of molecules come into contact, the interstitial space of exo-tetrahydrodicyclopentadiene will be likely to be occupied by parts of isopropylcyclohexane. The phenomenon leads to a closer distance between these molecules so that the negative values of VEm for binary mixtures of exo-tetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2) are observed. With the rising temperature, the molecular motion becomes fiercer and causes a slightly decrease of VEm at a certain composition. Distinctively, methyl laurate is a typical FAME (fatty acid methyl ester) F



Article

Table 5. Measured Densities (ρ) at Different Mole Fractions (x1 and x2) for the Ternary Mixtures of exoTetrahydrodicyclopentadiene (1) + Isopropylcyclohexane (2) + Methyl Laurate (3) at Temperatures T = (293.15−343.15) K and Pressure p = 0.1 MPaa ρ/g·cm−3 x1

x2

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

323.15 K

328.15 K

333.15 K

338.15 K

343.15 K

0.1003 0.1004 0.1007 0.1014 0.1008 0.1014 0.0999 0.1001 0.1999 0.2004 0.2064 0.2008 0.2005 0.2004 0.2008 0.3005 0.3002 0.3002 0.2999 0.2996 0.2988 0.3997 0.3996 0.4003 0.3998 0.4000 0.4998 0.4997 0.5001 0.4996 0.5991 0.5996 0.6017 0.6943 0.6993 0.7989

0.0999 0.2001 0.2998 0.3993 0.4995 0.5992 0.6998 0.8001 0.1006 0.1998 0.2982 0.4001 0.4996 0.5997 0.6990 0.1002 0.2000 0.3002 0.4003 0.5003 0.6017 0.1004 0.2010 0.3002 0.3994 0.5003 0.1000 0.2007 0.3005 0.4007 0.1005 0.2003 0.2985 0.0992 0.2008 0.1004

0.86818 0.86310 0.85773 0.85191 0.84555 0.83877 0.83132 0.82339 0.87226 0.86724 0.86220 0.85597 0.84971 0.84294 0.83573 0.87687 0.87188 0.86657 0.86078 0.85457 0.84798 0.88205 0.87716 0.87200 0.86659 0.86054 0.88793 0.88320 0.87824 0.87290 0.89457 0.89021 0.88586 0.90192 0.89835 0.91124

0.86428 0.85921 0.85384 0.84803 0.84167 0.83489 0.82745 0.81951 0.86835 0.86334 0.85831 0.85209 0.84582 0.83906 0.83184 0.87297 0.86798 0.86267 0.85689 0.85068 0.84408 0.87814 0.87326 0.86810 0.86269 0.85664 0.88402 0.87930 0.87434 0.86900 0.89065 0.88631 0.88195 0.89801 0.89444 0.90733

0.86036 0.85530 0.84995 0.84414 0.83778 0.83100 0.82356 0.81562 0.86444 0.85944 0.85442 0.84820 0.84193 0.83517 0.82793 0.86906 0.86408 0.85878 0.85300 0.84678 0.84018 0.87424 0.86936 0.86420 0.85879 0.85273 0.88011 0.87539 0.87044 0.86509 0.88674 0.88240 0.87805 0.89410 0.89053 0.90342

0.85645 0.85140 0.84605 0.84024 0.83389 0.82711 0.81967 0.81171 0.86052 0.85553 0.85051 0.84430 0.83803 0.83127 0.82403 0.86515 0.86018 0.85487 0.84910 0.84288 0.83626 0.87033 0.86545 0.86030 0.85488 0.84882 0.87620 0.87149 0.86653 0.86118 0.88283 0.87849 0.87414 0.89020 0.88662 0.89952

0.85253 0.84749 0.84214 0.83634 0.82999 0.82321 0.81576 0.80780 0.85660 0.85162 0.84661 0.84039 0.83413 0.82736 0.82011 0.86123 0.85626 0.85096 0.84518 0.83897 0.83234 0.86641 0.86153 0.85638 0.85096 0.84490 0.87227 0.86757 0.86260 0.85725 0.87890 0.87456 0.87020 0.88627 0.88270 0.89559

0.84861 0.84357 0.83823 0.83243 0.82608 0.81930 0.81185 0.80388 0.85268 0.84771 0.84269 0.83648 0.83021 0.82344 0.81618 0.85731 0.85235 0.84704 0.84126 0.83504 0.82841 0.86248 0.85761 0.85245 0.84704 0.84096 0.86834 0.86364 0.85867 0.85332 0.87497 0.87063 0.86627 0.88233 0.87876 0.89165

0.84469 0.83966 0.83432 0.82852 0.82217 0.81538 0.80793 0.79996 0.84875 0.84379 0.83877 0.83256 0.82629 0.81951 0.81225 0.85339 0.84842 0.84312 0.83734 0.83111 0.82448 0.85855 0.85368 0.84852 0.84310 0.83702 0.86440 0.85970 0.85474 0.84937 0.87103 0.86669 0.86232 0.87839 0.87481 0.88771

0.84076 0.83573 0.83040 0.82460 0.81825 0.81146 0.80400 0.79602 0.84483 0.83986 0.83485 0.82863 0.82236 0.81558 0.80831 0.84945 0.84449 0.83919 0.83340 0.82717 0.82053 0.85461 0.84974 0.84458 0.83916 0.83307 0.86046 0.85576 0.85079 0.84542 0.86709 0.86274 0.85837 0.87444 0.87086 0.88376

0.83683 0.83181 0.82647 0.82067 0.81432 0.80753 0.80007 0.79207 0.84089 0.83593 0.83091 0.82470 0.81843 0.81164 0.80436 0.84552 0.84055 0.83525 0.82946 0.82323 0.81657 0.85067 0.84580 0.84064 0.83521 0.82911 0.85652 0.85181 0.84684 0.84146 0.86314 0.85879 0.85441 0.87049 0.86690 0.87980

0.83289 0.82787 0.82254 0.81674 0.81038 0.80359 0.79612 0.78811 0.83695 0.83199 0.82697 0.82076 0.81448 0.80769 0.80039 0.84157 0.83661 0.83131 0.82552 0.81927 0.81261 0.84673 0.84185 0.83669 0.83125 0.82515 0.85257 0.84786 0.84288 0.83749 0.85918 0.85483 0.85044 0.86653 0.86294 0.87584

0.82895 0.82393 0.81860 0.81280 0.80644 0.79964 0.79216 0.78414 0.83301 0.82805 0.82303 0.81682 0.81053 0.80372 0.79642 0.83762 0.83266 0.82735 0.82156 0.81531 0.80863 0.84277 0.83790 0.83273 0.82729 0.82117 0.84861 0.84390 0.83892 0.83352 0.85522 0.85086 0.84647 0.86256 0.85896 0.87187

a

Standard uncertainties u are u(p) = 0.50 kPa, u(T) = 0.01 K, uc(x) = 0.0001, ur(ρ) = 0.0003.

For the binary mixture of exo-tetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2), a noticeable decrease in viscosities is given considering the lower interaction between two molecules, which is consistent with reported literature.29,30 With the increase of temperature, the reduced interaction results in the decrease of absolute Δη values at a certain composition. Volumetric and Viscometric Properties of the Ternary Mixtures. The experimental densities and viscosities of the ternary mixtures, exo-tetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2) + methyl laurate (3), over the entire composition range at different temperatures (T = 293.15− 343.15 K) are given in Tables 5 and 6, respectively. Likewise, the excess molar volumes (VEm) and viscosity deviations (Δη) of corresponding mixture samples are calculated according to eqs 3 and 4, which is presented in Tables S3 and S4, respectively. These data are fitted to the following equation (eq 7) Y123 = Y12 + Y13 + Y23 + Δ123

where Y123 refers to the excess molar volume or viscosity deviation of the ternary mixture. Y12, Y13, and Y23 refer to the corresponding contribution of three binary effect (i + j): exotetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2), exo-tetrahydrodicyclopentadiene (1) + methyl laurate (3), and isopropylcyclohexane (2) + methyl laurate (3), to the whole values of VEm or Δη, and are obtained by eq 5. Δ123 refers to the contribution of ternary effect, which is described with four typical semi-empirical equations (eqs 8−11) in this work. Nagata−Tamura Δ123 = x1x 2x3RT (B0 − B1x1 − B2 x 2 − B3x12 − B4 x 2 2 − B5x1x 2 − B6 x13 − B7 x 2 3 − B8x12x 2)

(8)

Cibulka Δ123 = x1x 2x3(C1 + C2x1 + C3x 2)

(7)

(9)

Singh G



Article

Table 6. Measured Viscosities (η) at Different Mole Fractions (x1 and x2) for the Ternary Mixtures of exoTetrahydrodicyclopentadiene (1) + Isopropylcyclohexane (2) + Methyl Laurate (3) at Temperatures T = (293.15−343.15) K and Pressure p = 0.1 MPaa η/mPa·s x1

x2

293.15 K

298.15 K

303.15 K

308.15 K

313.15 K

318.15 K

323.15 K

328.15 K

333.15 K

338.15 K

343.15 K

0.1003 0.1004 0.1007 0.1014 0.1008 0.1014 0.0999 0.1001 0.1999 0.2004 0.2064 0.2008 0.2005 0.2004 0.2008 0.3005 0.3002 0.3002 0.2999 0.2996 0.2988 0.3997 0.3996 0.4003 0.3998 0.4000 0.4998 0.4997 0.5001 0.4996 0.5991 0.5996 0.6017 0.6943 0.6993 0.7989

0.0999 0.2001 0.2998 0.3993 0.4995 0.5992 0.6998 0.8001 0.1006 0.1998 0.2982 0.4001 0.4996 0.5997 0.6990 0.1002 0.2000 0.3002 0.4003 0.5003 0.6017 0.1004 0.2010 0.3002 0.3994 0.5003 0.1000 0.2007 0.3005 0.4007 0.1005 0.2003 0.2985 0.0992 0.2008 0.1004

2.818 2.565 2.318 2.099 1.884 1.682 1.501 1.336 2.756 2.504 2.270 2.043 1.843 1.641 1.467 2.718 2.462 2.218 1.990 1.792 1.601 2.680 2.422 2.175 1.962 1.760 2.639 2.380 2.144 1.931 2.601 2.347 2.132 2.611 2.364 2.613

2.520 2.305 2.095 1.902 1.715 1.539 1.379 1.233 2.470 2.255 2.053 1.857 1.681 1.505 1.351 2.439 2.220 2.010 1.814 1.641 1.472 2.405 2.187 1.975 1.790 1.614 2.377 2.154 1.952 1.764 2.350 2.131 1.944 2.364 2.147 2.371

2.267 2.083 1.905 1.734 1.569 1.414 1.272 1.142 2.227 2.043 1.864 1.696 1.542 1.388 1.250 2.206 2.016 1.832 1.661 1.510 1.359 2.177 1.989 1.804 1.642 1.488 2.156 1.963 1.786 1.622 2.136 1.945 1.783 2.152 1.963 2.161

2.056 1.896 1.740 1.589 1.444 1.305 1.179 1.061 2.023 1.859 1.705 1.558 1.421 1.283 1.161 2.007 1.840 1.679 1.527 1.394 1.260 1.981 1.818 1.655 1.512 1.376 1.967 1.797 1.642 1.495 1.951 1.785 1.638 1.970 1.803 1.980

1.875 1.734 1.598 1.463 1.334 1.210 1.096 0.990 1.846 1.702 1.566 1.437 1.316 1.192 1.081 1.834 1.688 1.545 1.410 1.292 1.170 1.813 1.669 1.525 1.398 1.276 1.801 1.652 1.516 1.384 1.789 1.643 1.512 1.805 1.662 1.821

1.718 1.595 1.474 1.352 1.237 1.126 1.023 0.926 1.693 1.567 1.446 1.331 1.221 1.110 1.010 1.685 1.555 1.428 1.308 1.201 1.092 1.667 1.539 1.411 1.298 1.188 1.658 1.526 1.403 1.286 1.649 1.520 1.401 1.665 1.538 1.680

1.581 1.473 1.365 1.256 1.152 1.051 0.958 0.870 1.560 1.448 1.339 1.236 1.139 1.038 0.946 1.554 1.438 1.325 1.217 1.121 1.021 1.538 1.424 1.310 1.208 1.110 1.531 1.413 1.304 1.199 1.524 1.409 1.303 1.539 1.427 1.555

1.462 1.363 1.268 1.169 1.076 0.985 0.899 0.819 1.442 1.342 1.245 1.152 1.065 0.972 0.889 1.437 1.336 1.232 1.134 1.048 0.958 1.424 1.322 1.220 1.128 1.038 1.419 1.313 1.214 1.119 1.413 1.310 1.214 1.428 1.328 1.443

1.356 1.268 1.182 1.092 1.007 0.924 0.846 0.772 1.339 1.249 1.161 1.077 0.997 0.913 0.837 1.334 1.242 1.149 1.060 0.982 0.900 1.324 1.232 1.139 1.055 0.974 1.320 1.224 1.135 1.048 1.315 1.221 1.135 1.330 1.239 1.345

1.261 1.182 1.103 1.023 0.945 0.869 0.798 0.731 1.246 1.166 1.085 1.008 0.936 0.859 0.790 1.243 1.159 1.075 0.995 0.923 0.848 1.234 1.151 1.066 0.990 0.917 1.230 1.144 1.063 0.985 1.227 1.142 1.064 1.241 1.160 1.257

1.177 1.105 1.034 0.961 0.890 0.821 0.755 0.692 1.163 1.091 1.018 0.947 0.881 0.811 0.747 1.161 1.085 1.008 0.936 0.869 0.800 1.152 1.077 1.000 0.931 0.864 1.150 1.071 0.998 0.926 1.147 1.070 0.999 1.162 1.088 1.175

a

Standard uncertainties u are u(p) = 0.50 kPa, u(T) = 0.01 K, uc(x) = 0.0001, ur(η) = 0.01.

temperatures. Meanwhile, the values of VEm are almost all positive over the entire composition range, except for few negative values occurred in the methyl laurate-poor region. The answer to these observed phenomena can be involved in two factors: geometrical packing between different structural molecules and the physical interaction weakening between methyl laurate molecules. Figure 5 and Table S4 show that the negative values of Δη are obtained at each composition and measured temperature. Being the same as the binary mixtures, the absolute value of Δη for the ternary mixture also decreases with enhanced temperature, which is related with the weakening interaction between different molecules. Furthermore, according to the calculated deviations of four typical equations (Nagata−Tamura, Cibulka, Singh, and Redlich−Kister equations), there is no dramatic difference in the fitting ability of our studied mixture.

Δ123 = x1x 2x3[B1 + B2 x1(x 2 − x3) + B3x12(x3 − x 2)] (10)

Redlich−Kister Δ123 = x1x 2x3[A + B(x1 − x 2) + C(x 2 − x3) + D(x3 − x1) + E(x1 − x 2)2 + F(x 2 − x3)2 + G(x3 − x1)2 ]

(11)

where xi represents the mole fraction of component i; R and T represent the gas constant and thermodynamic temperature, respectively. The fitted coefficients (B, C, D, E, ..., G) of four semi-empirical equations and corresponding standard deviations (σ) calculated by the least-squares method and F-test are shown in Tables S6−S9. As a sample, the correlated curves of VEm and Δη by fitting Nagata−Tamura equation at 298.15 and 343.15 K are plotted in Figures 4 and 5, respectively. It can be seen that the VEm of ternary mixture has a similar variation trend at different

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CONCLUSIONS Densities and viscosities of the ternary mixtures of exotetrahydrodicyclopentadiene + isopropylcyclohexane + methyl H



Article

Figure 5. Curves of Δη/mPa·s for the ternary system exotetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2) + methyl laurate (3) correlated by the Nagata−Tamura equation at (a) T = 298.15 K; (b) T = 343.15 K.

Figure 4. Curves of VEm/cm3·mol−1 for the ternary system exotetrahydrodicyclopentadiene (1) + isopropylcyclohexane (2) + methyl laurate (3) correlated by the Nagata−Tamura equation at (a) T = 298.15 K; (b) T = 343.15 K.

rising temperature. These results will be useful for the application of biodiesel as jet fuel extenders.

laurate and three corresponding binary mixtures exo-tetrahydrodicyclopentadiene + isopropylcyclohexane; exo-tetrahydrodicyclopentadiene + methyl laurate; and isopropylcyclohexane + methyl laurate were measured at eleven different temperatures T = (293.15−343.15) K and atmospheric pressure p = 0.1 MPa. Additionally, the excess molar volumes (VEm) and viscosity deviations (Δη) of these mixtures were calculated based on these obtained data. The VEm and Δη with a composition of binary mixtures were fitted to the Redlich− Kister equation, and those of the ternary mixture were correlated to four semiempirical equations (Nagata−Tamura, Cibulka, Singh, and Redlich−Kister) satisfactorily. The values of VEm were negative for the binary mixture exo-tetrahydrodicyclopentadiene + isopropylcyclohexane, while the positive values were shown for other binary mixtures and mostly ternary mixtures. These observed phenomena can be ascribed to structure accommodation and interaction variation during the mixing process. On the other hand, the Δη values are all negative for both binary and ternary mixtures over the entire composition range, and the absolute values decreased with

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00397. Values of excess molar volumes (VEm), viscosity deviations (Δη) for binary mixtures, and ternary mixtures and the coefficients and deviations of VEm and Δη with the semi-empirical equation for binary and ternary mixtures (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: 86-571-88981416. Fax: +86-571-88981416. ORCID

Yongsheng Guo: 0000-0001-7609-1891 Wenjun Fang: 0000-0002-5610-1623 I



Article

Funding

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The authors are grateful for financial support from the National Natural Science Foundation of China (grant nos. J1210042, 21173191). Notes

The authors declare no competing financial interest.

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